This invention relates to seismic exploration and more particularly to a method of filtering for removing coherent noise from seismic traces. In seismic exploration, it is common practice to deploy a large array of geophones on the surface of the earth and to record the vibrations of the earth at each geophone location to obtain a collection of seismic traces. The traces are sampled and recorded for further processing. When the vibrations so recorded are caused by a seismic source activated at a known time and location, the recorded data can be processed by a computer in known ways to produce an image of the subsurface. The image thus produced is commonly interpreted by geophysicists to detect the possible presence of valuable hydrocarbons.
Seismograms are commonly recorded as digital samples representing the amplitude of a received seismic signal as a function of time. Since seismograms are usually obtained along a line of exploration on the surface of the earth, the digital samples can be formed into an array (t-x) with each sample in the array representing the amplitude of the seismic signal as a function of time (t) and horizontal distance (x). When such arrays are visually reproduced, by plotting or the like, seismic sections are produced. A seismic section depicts the subsurface layering of a section of the earth. It is the principal tool which the geophysicist studies to determine the nature of the earth's subsurface formation. Before an array of seismic samples or traces can be converted into a seismic section for interpretation by geophysicists, however, the array must be extensively processed to remove noise and make reflection events discernable.
In the processing of seismograms, t-x arrays are sometimes transformed into arrays of complex numbers as a function of frequency (f) and wavenumber (k). This is commonly referred to as a "frequency-wavenumber" or "f-k" transformation. The f-k transformation has been used as a tool to study and filter seismic data. F-k transforms are routinely used to represent data collected by large arrays of sensors, including seismic data. Usually the f-k representations are computed by fast Fourier transforms. The resulting data representations are parameterized by frequencies, wavenumbers (spatial frequencies), amplitudes, and phases. In particular, for each frequency there is a collection of wavenumbers, and for each frequency-wavenumber pair there is a complex number (an amplitude and a phase). Among various applications of this representation are spectrum analysis (displaying the amplitude squared as a function of frequency and wavenumber) and filtering in the frequency-wavenumber domain. F-k spectrum analysis and filtering are particularly important when seismic data are contaminated by large amplitude coherent noise which obscures geologically significant signals. Frequently the coherent noise occupies a different part of the f-k spectrum than the signals. In such cases f-k filtering can potentially be used to attenuate the coherent noise thus revealing the signals for interpretation.
In U.S. Pat. No. 4,218,765 to Kinkade, seismic traces are transformed to an f-k array and filtering is performed on the traces in the f-k domain. In U.S. Pat. No. 4,380,059 to Ruehle, multiple reflections are filtered from seismograms by transforming them into an f-k array representing amplitude as function of frequency and wavenumber. In Ruehle, the f-k array of the seismograms is filtered by weighting all samples with the inverse of the f-k transform of the multiple reflections. In U.S. Pat. No. 4,594,693 to Pann et al, seismic trace interpolation is carried out by inserting zero amplitude traces between the seismic traces in a section where spatial aliasing is a problem. The traces are then transformed into an f-k array. The f-k array is filtered to reject samples in a region of frequency and wavenumber which exhibits aliasing. The filtered f-k array is then transformed back into a seismic section representing amplitude as a function of time and distance. While f-k filtering is a very effective means of attenuating coherent noise from seismic traces, it is not the most optimal method in the sense of optimally preserving signal and rejecting noise. Taper zones between the noise and signal in the f-k domain have to be chosen by the geophysicist. If the taper zone is too small sidelobes will appear in the filtered seismic traces. If the taper zone is too large signal may be removed as well as the coherent noise or the coherent noise will not be significantly removed.
It is, therefore, an object of the present invention to provide for a new and improved method of filtering seismic traces to remove coherent noise that overcomes limitations present in f-k filtering methods.